Superconductivity, plasmas and the Darwin Hamiltonian approach

Information about research on superconductivity and
plasmas based on the Darwin Hamiltonian approach can be found in the following
papers and links. The main result is that superconductivity is the phase transition
caused by the Darwin (-Breit) term in the Hamiltonian, i.e. the attraction
between parallel currents. Alternatively, the superconducitvity phase transition may be said to be caused by the energy lowering resulting from the correlation of electron momenta on the Fermi surface. Phonons only play a destructive role and partly
determine the transition temperature by destroying the correlation of electron
momenta at higher temperatures.

A short history of the idea:

The famous russian physicist J. Frenkel (Yacov Ilich Frenkel, 1894-1952) originally suggested the magnetic explanation of superconductivity in 1933. The same year, 1933, Hans Bethe and H. Fr÷hlich published a paper claiming that Frenkel's explanation had to be wrong. Their argument is classical and based on a version of the Darwin Hamiltonian (Charles Galton Darwin, 1887-1962) derived by the authors, independently of Darwin (1920). Later the german physicist Heinrich Welker (1912-1981) again suggested a magnetic explanation of superconductivity (1939). He tried to get around the problems suggested by Bethe and Fr÷hlich by discussing quantum effects, in particular exchange. Welker also gave an elegant explanation of the Meissner effect (1938). Thus ended the early attempts at a magnetic theory of superconductivity.
As I see it the error in the Bethe-Fr÷hlich paper is the purely classical treatment. Electrons produce and interact with magnetic fields via the expectation value of their current density. The majority of electrons in a metal occupy states with real wave functions (zero current density) and thus neither produce nor interact with a magnetic field. The remaining few that do are the ones that are part of the superconducting condensate. I therefore think that Fr÷hlich and BCS are wrong; phonons do not cause superconductivity, they destroy it. Magnetic interaction is the true cause, but no one knows how to calculate accurately and quantum mechanically, the properties of systems of very many particles interacting magnetically. Order of magnitude estimates and simple approximations and idealizations, however, support the Frenkel-Welker-EssÚn theory.

Here is a list of my (Hanno EssÚn's) published papers on the subject. There are links to pdf-files of the papers (note that these are not exact versions of the published papers; they may differ in minor details).

Direct numerical simulation shows that the Darwin interaction can cause a phase transition. This is done in the following very relevant and important paper:
Vishal Mehra and Jayme De Luca
Long range magnetic order and the Darwin Lagrangian
Phys. Rev. E 61 (2000) pp.1199-1205. (in: http://www.arxiv.org/abs/cond-mat/9909030)